# Representation Theory and Categorification Seminar (Fall 2024)

This is a continuation of last year's learning/research seminar on representation theory, often with an eye towards categorification. Talks will likely be disconnected talks from across representation theory and categorifcation, reflective of what the speaker is currently interested in working on/exploring; in particular this seminar is not cumulative and you are welcome to attend whatever talk you find interesting. There may be talks relating to affine Hecke algebras, KLR(W?) algebras, quantum affine algebras, Soergel bimodules, etc..

Talks will roughly be 1.25-1.5 hours, e.g. 45 minutes followed by a 5 minute break, followed by 45 more minutes. Please email Fan or Alvaro at fz2326@columbia.edu or alm2297@columbia.edu if you'd like to give a talk!

- Organizers: Davis Lazowski, Alvaro Martinez, Che Shen, Fan Zhou
- When: Thursday 4:40pm -- 6:10pm
- Where: Math Room 528

#### Schedule

- 09/05
- Speaker: Everyone
- Title:
** Logistics/Information **

Abstract: Just for headcount and gauging where participants' interests are.
- 09/12
- Speaker: Igor Chaban
- Title:
** Introduction to (type A) quantum groups **

Abstract: I will give the Drinfeld-Jimbo definition of a quantum group, corresponding to a simple Lie algebra. It will be shown that it has a Hopf algebra structure providing a 1-parameter deformation of universal enveloping algebra. Then I explain the classification of finite dimensional representations of U_q(sl_2) and sketch the general case.
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